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Concept · from MIT 2.003SC Engineering Dynamics

Vibration Analysis by Mode Superposition

About these materials

MIT's own material for this topic, in MIT's order: Vibration Analysis by Mode Superposition.

Source: MIT OpenCourseWare 2.003SC Engineering Dynamics, Fall 2011, Prof. J. Kim Vandiver, Prof. David Gossard — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Order: the items appear in the order MIT's own session page lists them. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

MIT's session, in MIT's order

MIT 2.003SC · · This session on MIT OpenCourseWare ↗

Session Overview

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Videos · Lecture Videos

  1. Lecture 25: Modal Analysis: Response to IC's and to Harmonic ForcesLecture video · transcript Watch
  2. Outline of the final three lecturesLecture clip · 0:21–1:18:29 · 1:18:08 long · transcript Watch
  3. Response to initial conditions and the use of Rayleigh damping to model modal damping ratiosLecture clip · 3:32–1:18:29 · 1:14:57 long · transcript Watch
  4. Steady state response to harmonic excitation by the method of modal analysisLecture clip · 43:53–1:18:29 · 34:36 long · transcript Watch
  5. Demonstration of the response of a string to harmonic excitationLecture clip · 1:02:11–1:18:29 · 16:18 long · transcript Watch
  6. Demonstration of the response of a string to initial deflectionLecture clip · 1:06:40–1:18:29 · 11:49 long · transcript Watch
  7. Direct method for assembling the stiffness of an N DOF systemLecture clip · 1:09:36–1:18:29 · 8:53 long · transcript Watch
  8. Lecture 26: Response of 2-DOF Systems by the Use of Transfer FunctionsLecture video · transcript Watch
  9. Discussion of problem set concept questionsLecture clip · 0:21–1:21:30 · 1:21:09 long · transcript Watch
  10. Review of the use of a transfer function to analyze the response of a single DOF system to harmonic inputLecture clip · 7:11–1:21:30 · 1:14:19 long · transcript Watch
  11. Analysis of the response of a 2-DOF system to harmonic excitation by means of transfer functions and the introduction of the application of the dynamic absorber to mitigate problem vibrationLecture clip · 14:12–1:21:30 · 1:07:18 long · transcript Watch
  12. Demonstration of a dynamic absorber using a strobe and a vibrating beamLecture clip · 1:07:30–1:21:30 · 14:00 long · transcript Watch
  13. Questions and answers: discussion of helicopter video and the 300 ton dynamic absorber in the Hancock buildingLecture clip · 1:12:42–1:21:30 · 8:48 long · transcript Watch
  14. Lecture 27: Vibration of Continuous Structures: Strings, Beams, Rods, etc.Lecture video · transcript Watch
  15. Demonstration of wave propagation on a long stringLecture clip · 0:25–1:12:13 · 1:11:48 long · transcript Watch
  16. My personal research area: Flow-induced vibration of long strings and beams in fluid flowLecture clip · 3:30–1:12:13 · 1:08:43 long · transcript Watch
  17. Derivation of the "wave equation"Lecture clip · 15:45–1:12:13 · 56:28 long · transcript Watch
  18. Natural frequencies and mode shapes of the string under tension-with demonstrationLecture clip · 26:17–1:12:13 · 45:56 long · transcript Watch
  19. Application of the wave equation to rods, organ pipes, shower stalls with demonstrationsLecture clip · 45:23–1:12:13 · 26:50 long · transcript Watch
  20. The vibration of beams: natural frequencies as a function of boundary conditions, dispersion in wave propagationLecture clip · 55:45–1:12:13 · 16:28 long · transcript Watch

Videos · Recitation Video and Notes

  1. Recitation 12: Modal Analysis of a Double Pendulum SystemProblem-solving video · transcript Watch

Check Yourself · Concept Question Answer Key and Problem Set Solutions

Where this sits in MIT 2.003SC

Open this session in the full course 2.003SC Engineering Dynamics: all units →

MIT OpenCourseWare, Prof. J. Kim Vandiver, Prof. David Gossard, 2.003SC Engineering Dynamics, Fall 2011.

License: CC BY-NC-SA 4.0 · Edition: Fall 2011 · Open the original course on OCW ↗

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